## Faster sorting and routing on grids with diagonals (1994)

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Venue: | Proceedings of the 11th Symposium on Theoretical Aspects of Computer Science, number 775 in Lecture Notes in Computer Science |

Citations: | 8 - 4 self |

### BibTeX

@INPROCEEDINGS{Kunde94fastersorting,

author = {Manfred Kunde and Rolf Niedermeier and Peter Rossmanith},

title = {Faster sorting and routing on grids with diagonals},

booktitle = {Proceedings of the 11th Symposium on Theoretical Aspects of Computer Science, number 775 in Lecture Notes in Computer Science},

year = {1994},

pages = {225--236},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

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### Abstract

### Citations

1363 |
Introduction to Parallel Algorithms and Architectures: Arrays
- Leighton
(Show Context)
Citation Context ...ome open questions. \Delta 3 2. Preliminaries In this section we present some basic definitions and notations we use in this paper. Leighton presents further details and motivation in his recent book =-=[9]-=-. A processor grid with diagonals is a network of n 2 processors arranged in an n \Theta n array. Processor (r; c) in row r and column c on the grid is directly connected by a bi-directional communica... |

259 |
Sorting and searching. In Volume 3 of The Art of Computer Programming ( printing
- Knuth
- 1973
(Show Context)
Citation Context ...ay that all places in block i have smaller indices than all places in block i + 1. We call such an indexing continuous. To see the correctness of the following sorting method we use the 0-1 principle =-=[5, 9]-=-. In a first step we sprinkle all data all over the mesh in order to get approximately the same number of ones into each block. We start by sorting each block individually as follows. The ith brick ge... |

92 | Sorting on a Mesh Connected Parallel Computer - Thompson, Kung - 1977 |

90 | An optical sorting algorithm for meshconnected computers - Schnorr, Shamir - 1986 |

88 | Systolic arrays for VLSI - Kung, Leiserson - 1978 |

52 |
Methods for message routing in parallel machines
- Leighton
- 1992
(Show Context)
Citation Context ...lem one can supply each packet with an index of its destination processor. In this manner the full h-h routing problem becomes an h-h sorting problem. The model of computation is the conventional one =-=[9, 10]-=-, where only nearest neighbors exchange data. In one step a communication channel can transport at most one packet (as an atomic unit) in each direction. Processors may store more than h packets, but ... |

37 | Introduction to the Configurable Highly Parallel Computer - Snyder |

36 |
Matching the bisection bound for routing and sorting on the mesh
- Kaufmann, Rajasekaran, et al.
- 1992
(Show Context)
Citation Context ...s well as randomized algorithms (the latter ones are marked with an asterisk). We omit all sublinear terms, which are of no importance for the asymptotic complexity. Kaufmann, Rajasekaran, and Sibeyn =-=[2, 3, 4]-=- gave randomized algorithms for h-h problems on an n \Theta n mesh that need hn=2 + o(hn) steps if hs8. We showed that it is possible to solve the h-h routing and sorting problems within the same numb... |

32 |
A 2n \Gamma 2 Step Algorithm for Routing in an n \Theta n Array with Constant Size Queues
- Leighton, Makedon, et al.
- 1989
(Show Context)
Citation Context ...tly, Kaklamanis and Krizanc [1] presented a randomized algorithm (needing constant buffer size) that sorts in only 2n + o(n) steps with high probability. For 1-1 routing Leighton, Makedon, and Tollis =-=[11]-=- presented optimal deterministic algorithms (with constant buffer size) that exactly match the distance bound of 2n \Gamma 2 steps. Rajasekaran and Overholt [14] further reduced the buffer size. We pr... |

32 | Constant Queue Routing on a Mesh
- Rajasekaran, Overholt
- 1990
(Show Context)
Citation Context ... routing Leighton, Makedon, and Tollis [11] presented optimal deterministic algorithms (with constant buffer size) that exactly match the distance bound of 2n \Gamma 2 steps. Rajasekaran and Overholt =-=[14]-=- further reduced the buffer size. We present algorithms for grids with diagonals that need 1:33n + o(n) steps for 1-1 sorting and 1:11n + o(n) steps for routing. For grids with diagonals we summarize ... |

22 |
Optimal sorting on mesh-connected processor arrays
- Kaklamanis, Krizanc
- 1992
(Show Context)
Citation Context ...fastest ones need 3n + o(n) steps [12, 15, 17]. For buffer size 2 we showed how to solve the 1-1 sorting problem deterministically in 2:5n + o(n) transport steps [6]. Recently, Kaklamanis and Krizanc =-=[1]-=- presented a randomized algorithm (needing constant buffer size) that sorts in only 2n + o(n) steps with high probability. For 1-1 routing Leighton, Makedon, and Tollis [11] presented optimal determin... |

12 | Optimal MultiPacket Routing on the Torus
- Kaufmann, Sibeyn
- 1992
(Show Context)
Citation Context ...s well as randomized algorithms (the latter ones are marked with an asterisk). We omit all sublinear terms, which are of no importance for the asymptotic complexity. Kaufmann, Rajasekaran, and Sibeyn =-=[2, 3, 4]-=- gave randomized algorithms for h-h problems on an n \Theta n mesh that need hn=2 + o(hn) steps if hs8. We showed that it is possible to solve the h-h routing and sorting problems within the same numb... |

10 |
The Distance Bound for Sorting on Mesh Connected Proces- sor Arrays is Tight
- Ma, Sen, et al.
- 1986
(Show Context)
Citation Context ...imensional n \Theta n meshes without diagonals 1-1 problems have been studied for more than twenty years. Several 1-1 sorting algorithms exist for buffer size 1. The fastest ones need 3n + o(n) steps =-=[12, 15, 17]-=-. For buffer size 2 we showed how to solve the 1-1 sorting problem deterministically in 2:5n + o(n) transport steps [6]. Recently, Kaklamanis and Krizanc [1] presented a randomized algorithm (needing ... |

9 |
Reducing Communication Costs for Sorting on MeshConnected and Linearly Connected Parallel Computers
- Park, Balasubramanian
- 1990
(Show Context)
Citation Context ...esults Problem with diagonals Without diagonals 1-1 routing 1:11n 2n Leighton et al. [11] 1-1 sorting 1:33n 2:5n Kunde [6] 2n* Kaklamanis and Krizanc [1] 2-2 routing 1:67n 3n Park and Balasubramanian =-=[13]-=- 2:67n* Sibeyn and Kaufmann [3] 2-2 sorting 1:67n 3n Park and Balasubramanian [13] 4-4 routing 2n 4n Kunde [6] 2n* Kaufmann et al. [2] 4-4 sorting 2n 4n Kunde [6] 3n* Sibeyn and Kaufmann [3] 8-8 sorti... |

7 |
gossiping on grids and tori: Sorting and routing match the bisection bound deterministically
- Block
- 1993
(Show Context)
Citation Context ...r h-h problems on an n \Theta n mesh that need hn=2 + o(hn) steps if hs8. We showed that it is possible to solve the h-h routing and sorting problems within the same number of steps deterministically =-=[7]-=-. These results are optimal, since they match the simple bisection bound of hn=2 steps valid for this type of architecture. On meshes with diagonals we reach 2hn=9 + O(hn 2=3 ) steps for deterministic... |

1 |
Optimal k-k sorting on meshes and tori
- Kaufmann, Sibeyn
- 1993
(Show Context)
Citation Context ...s well as randomized algorithms (the latter ones are marked with an asterisk). We omit all sublinear terms, which are of no importance for the asymptotic complexity. Kaufmann, Rajasekaran, and Sibeyn =-=[2, 3, 4]-=- gave randomized algorithms for h-h problems on an n \Theta n mesh that need hn=2 + o(hn) steps if hs8. We showed that it is possible to solve the h-h routing and sorting problems within the same numb... |

1 |
Concentrated regular data streans on grids: Sorting and routing near to the bisection bound
- Kunde
- 1991
(Show Context)
Citation Context ...gorithms exist for buffer size 1. The fastest ones need 3n + o(n) steps [12, 15, 17]. For buffer size 2 we showed how to solve the 1-1 sorting problem deterministically in 2:5n + o(n) transport steps =-=[6]-=-. Recently, Kaklamanis and Krizanc [1] presented a randomized algorithm (needing constant buffer size) that sorts in only 2n + o(n) steps with high probability. For 1-1 routing Leighton, Makedon, and ... |